Recovering outcomes when you do not trust your recovery model

Every de-censoring result below this one on the frontier — the exact kernel, the adaptive premium, even the screening negative result — assumes the recovery law is known: how much a recovery costs, how likely it is to succeed, what it tends to return. In the field that law is estimated from history, and a plan that is optimal under the estimate can be brittle under the truth. What should you recover when you do not fully trust your model of recovery? This project is the robustness question, and it is at the idea stage.

Three early findings

We work over an ambiguity set of recovery laws and ask for a de-censoring selection that behaves well across the whole set rather than at a single point estimate. Three structural observations have survived contact with the flagship kernel so far. None is validated.

A refusal behaviour under the worst-case objective. Under a worst-case objective, the robust policy refuses to buy evidence whose value the ambiguity set can drive to zero. This is not a bug; it is the objective doing its job. But it is severe: if the ambiguity set is wide enough to contain a law under which a recovery is worthless, the worst-case objective will decline that recovery even when it is valuable under almost every other law in the set. Taken to its conclusion, a broad enough ambiguity set produces a policy that refuses all acquisition. A robust de-censoring method that never recovers anything is safe and useless.

The classical maximin-versus-minimax-regret separation, instantiated on our kernel. That minimax-regret and maximin (max–min) can prescribe different actions is a classical fact of decision theory under ambiguity, not a finding of ours: Savage (1951) introduced the minimax-regret criterion precisely to escape the excessive conservatism of maximin, and Milnor (1954) axiomatised how the two criteria come apart. What is ours is the instantiation. Switching the objective from worst-case value to worst-case regret changes the behaviour qualitatively on the flagship kernel: regret rewards evidence that protects you from being badly wrong, not only evidence with a guaranteed worst-case payoff, so a minimax-regret policy acquires in cases where max–min refuses. This matters because the whole point of de-censoring is to buy information, and an objective that structurally suppresses acquisition defeats the exercise. Regret appears to be the right robustness objective here for exactly that reason, though “appears to be” is the correct strength of claim at this stage.

One tempting shortcut is provably unsound. The attractive move is to collapse the ambiguity set to a single law and reuse the existing screen once, rather than reasoning over the set. We can rule this out exactly: the robust selection is strictly better than anything obtainable that way. The construction stays in the lab; the consequence is what matters, and the robustness has to be carried through the combinatorial selection, not pushed outside it, which connects this project to the same lesson the screening negative result taught, that the cheap outer loop is often an illusion.

What has to happen next

Two things, in order. First, a calibrated ambiguity set: an uncalibrated set makes the robust policy either vacuous (too narrow, no robustness) or paranoid (too wide, the refusal mechanism eats everything). Calibrating it from recovery history, with a stated coverage guarantee, is the work. Second, a prospective test of robust validity: does a minimax-regret selection hold up when the recovery law turns out to be wrong in the way the ambiguity set anticipated? Until both exist, this is a well-posed research direction with three suggestive structural findings — no more, and we will not dress it as more.